Free-encoder positioning system using acoustic features and imu

ABSTRACT

Using various techniques, a position of a probe assembly of a non-destructive inspection system, such as a phase array ultrasonic testing (PAUT) system, can be determined using the acoustic capability of the probe assembly and an inertial measurement unit (IMU) sensor, e.g., including a gyroscope and an accelerometer, without relying on a complex encoding mechanism. The IMU sensor can provide an estimate of a current location of the probe assembly, which can be confirmed by the probe assembly, using an acoustic signal. In this manner, the data acquired from the IMU sensor and the probe assembly can be used in a complementary manner.

CLAIM OF PRIORITY

This application claims the benefit of priority of U.S. ProvisionalPatent Application Ser. No. 63/178,698, titled “FREE-ENCODER POSITIONINGSYSTEM USING ACOUSTIC FEATURES AND IMU” to Nicolas Badeau et al., filedon Apr. 23, 2021, the entire contents of which being incorporated hereinby reference.

FIELD OF THE DISCLOSURE

This document pertains generally, but not by way of limitation, tonon-destructive testing and inspection devices (NDT/NDI).

BACKGROUND

Some non-destructive inspection systems, such as phase array ultrasonictesting (PAUT), can generate an image of what is inside the materialunder test, e.g., components or parts. Inspection of complex componentsor parts by non-destructive inspection can be quite challenging asfinding and sizing a flaw or defect depends heavily on probe positioningduring inspection. To generate an accurate image, the inspection systemshould know the position of its probe assembly relative to the materialunder test.

Many non-destructive inspection systems use mechanical systems to encodethe position and the movement of the probe assembly. For example, atwo-axis encoding system can be used to inspect a straight tube, with aseparate encoder for each axis. With such a two-axis encoding system,the non-destructive inspection system can determine the position of theprobe assembly using the knowledge that a straight tube is underinspection. However, such a two-axis encoding system can only be used toinspect a straight tube, for example.

Complex encoding mechanisms are often necessary for corrosion or weldinspection. For example, shaped components such as nozzles, elbows, andthe like can require an encoding system different than that used forinspecting straight tubes.

SUMMARY OF THE DISCLOSURE

Using various techniques of this disclosure, a position of a probeassembly of a non-destructive inspection system, such as a phase arrayultrasonic testing (PAUT) system, can be determined using the acousticcapability of the probe assembly and an inertial measurement unit (IMU)sensor, e.g., including a gyroscope and an accelerometer, withoutrelying on a complex encoding mechanism. The IMU sensor can provide anestimate of a current location of the probe assembly, which can beconfirmed by the probe assembly, using an acoustic signal. In thismanner, the data acquired from the IMU sensor and the probe assembly canbe used in a complementary manner.

In some aspects, this disclosure is directed to a method of estimating aposition of a probe assembly of a non-destructive inspection system, theprobe assembly positioned on a material and in communication with aninertial measurement unit (IMU) sensor, the method comprising:acquiring, at a first position of the probe assembly, a first acousticdata signal of the material using the probe assembly; acquiring, at asecond position of the probe assembly, a second acoustic data signal ofthe material using the probe assembly; determining a first estimate of adisplacement of the probe assembly between the first and secondpositions using the first and second acoustic data signals; determininga second estimate of the displacement of the probe assembly between thefirst and second positions using a signal from the IMU sensor; combiningthe first and second estimates of displacements; estimating, using thecombination, a motion of the probe assembly; and generating, using theestimated motion, the second position of the probe assembly.

In some aspects, this disclosure is directed to an ultrasound inspectionsystem for estimating a position of an ultrasonic probe assembly of anon-destructive inspection system, the system comprising: the ultrasonicprobe assembly to be positioned on a material and in communication withan inertial measurement unit (IMU) sensor; and a processor configuredto: acquire, at a first position of the probe assembly, a first acousticdata signal of the material using the probe assembly; acquire, at asecond position of the probe assembly, a second acoustic data signal ofthe material using the probe assembly; determine a first estimate of adisplacement of the probe assembly between the first and secondpositions using the first and second acoustic data signals; determine asecond estimate of the displacement of the probe assembly between thefirst and second positions using a signal from the IMU sensor; combinethe first and second estimates of displacements; estimate, using thecombination, a motion of the probe assembly; and generate, using theestimated motion, the second position of the probe assembly.

This overview is intended to provide an overview of subject matter ofthe present patent application. It is not intended to provide anexclusive or exhaustive explanation of the invention. The detaileddescription is included to provide further information about the presentpatent application.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, which are not necessarily drawn to scale, like numeralsmay describe similar components in different views. Like numerals havingdifferent letter suffixes may represent different instances of similarcomponents. The drawings illustrate generally, by way of example, butnot by way of limitation, various embodiments discussed in the presentdocument.

FIG. 1 illustrates generally an example of an acoustic inspectionsystem, such as can be used to perform one or more techniques describedherein.

FIG. 2 is a conceptual drawing graphically illustrating a technique totrack a position of a probe assembly of a non-destructive inspectionsystem, such as a phase array ultrasonic testing (PAUT) system, relativeto the surface of the component being inspected, using varioustechniques of this disclosure.

FIGS. 3A-3F graphically depict an example of estimating a position of aprobe assembly of a non-destructive inspection system using atwo-dimensional (2D) matrix array and corrosion mapping.

FIG. 4 is a flow diagram depicting an example of estimating a positionof a probe assembly of a non-destructive inspection system using atwo-dimensional (2D) matrix array and feature mapping, such ascorrosion, without prediction.

FIG. 5 is a flow diagram depicting an example of estimating a positionof a probe assembly of a non-destructive inspection system using atwo-dimensional (2D) matrix array and corrosion mapping, withprediction.

FIG. 6 is a conceptual diagram illustration an example of using SAFTprinciples to track a position of a probe assembly of a non-destructiveinspection system, such as a phase array ultrasonic testing (PAUT)system, relative to the surface of the component being inspected usingvarious techniques of this disclosure.

FIG. 7 is a flow diagram depicting an example of estimating a positionof a probe assembly of an NDT system using an ultrasonic probe arraypositioned on a material and in communication with an IMU sensor, inaccordance with this disclosure.

FIG. 8 is an example of a linear array that can be used to implementvarious techniques of this disclosure. The linear array 800 shown canform part of the transducer array 152 of FIG. 1.

FIG. 9 is an example of a two-dimensional (2D) matrix array that can beused to implement various techniques of this disclosure. Thetwo-dimensional (2D) matrix array 900 shown can form part of thetransducer array 152 of FIG. 1.

DETAILED DESCRIPTION

Complex encoding mechanisms are often necessary for corrosion or weldinspection of irregularly shaped components such as nozzles, elbows, andthe like. Such an encoding system can be different than that used forinspecting straight tubes due to the geometries of the components beinginspected. Each shaped component can require a different encodingmechanism. For example, an encoding system for a nozzle is likelydifferent than an encoding system for an elbow.

The present inventors have recognized that eliminating the need forusing complex encoding systems, or even relatively simple encodingsystems such as the Mini-Wheel™ encoder available from Olympus, canreduce inspection complexity and time. The present inventors haverecognized the need for a technique to track a position of a probeassembly of a non-destructive inspection system, such as a phase arrayultrasonic testing (PAUT) system, relative to the component or materialbeing inspected.

Using various techniques of this disclosure, a position of a probeassembly of a non-destructive inspection system, such as a phase arrayultrasonic testing (PAUT) system, can be determined using the acousticcapability of the probe assembly and an inertial measurement unit (IMU)sensor, e.g., including a gyroscope and an accelerometer, withoutrelying on a complex encoding mechanism. As described in detail below,the IMU sensor can provide an estimate of a current location of theprobe assembly, which can be confirmed by the probe assembly, using anacoustic signal. In this manner, the data acquired from the IMU sensorand the probe assembly can be used in a complementary manner.

FIG. 1 illustrates generally an example of an acoustic inspection system100, such as can be used to perform one or more techniques describedherein. The acoustic inspection system 100 can perform ultrasonic NDTtechniques. The acoustic inspection system 100 of FIG. 1 is an exampleof an acoustic imaging modality, such as an acoustic phased arraysystem, that can implement various techniques of this disclosure.

The inspection system 100, e.g., an ultrasound inspection system, caninclude a test instrument 140, such as a hand-held or portable assembly.The test instrument 140 can be electrically coupled to a probe assembly,such as using a multi-conductor interconnect 130. The electricalcoupling can be a wired connection or a wireless connection. The probeassembly 150 can include one or more electroacoustic transducers, suchas a transducer array 152 including respective transducers 154A through154N. The transducers array can follow a linear or curved contour or caninclude an array of elements extending in two axes, such as providing amatrix of transducer elements. The elements need not be square infootprint or arranged along a straight-line axis. Element size and pitchcan be varied according to the inspection application.

In some examples, the probe assembly 150 can include an inertialmeasurement unit (IMU) sensor 153, e.g., including a gyroscope and anaccelerometer, e.g., an encoder or device, to implement encoder-likefunctions. The IMU sensor 153 can be a micro-electromechanical system(MEMS) device, for example. The gyroscope of the IMU sensor 153 canprovide information of an angle of the probe assembly 150 and theaccelerometer can provide information of an acceleration of the probeassembly 150. In some examples, the IMU sensor 153 can be integratedwith the probe assembly 150. In other examples, the IMU sensor 153 canbe a separate component affixed to the probe assembly 150. As describedin detail below, the IMU sensor 153 can provide an estimate of a currentlocation of the probe assembly 150, which can be confirmed by the probeassembly 150, using an acoustic signal.

A modular probe assembly 150 configuration can be used, such as to allowa test instrument 140 to be used with various probe assemblies 150. In anon-limiting example, the transducer array 152 can include piezoelectrictransducers, such as can be acoustically coupled to a target 158 (e.g.,an object under test) through a coupling medium 156. In other examples,capacitive micromachined ultrasonic transducer (CMUT) arrays can beused. The coupling medium can include a fluid or gel or a solid membrane(e.g., an elastomer or other polymer material), or a combination offluid, gel, or solid structures. The wedge structures can include arigid thermoset polymer having known acoustic propagationcharacteristics (for example, Rexolite® available from C-Lec PlasticsInc.), and water can be injected between the wedge and the structureunder test as a coupling medium 156 during testing.

The test instrument 140 can include digital and analog circuitry, suchas a front-end circuit 122 including one or more transmit signal chains,receive signal chains, or switching circuitry (e.g., transmit/receiveswitching circuitry). The transmit signal chain can include amplifierand filter circuitry, such as to provide transmit pulses for deliverythrough an interconnect 130 to a probe assembly 150 for insonificationof the target 158, such as to image or otherwise detect a flaw 160 on orwithin the target 158 structure by receiving scattered or reflectedacoustic energy elicited in response to the insonification.

Although FIG. 1 shows a single probe assembly 150 and a singletransducer array 152, other configurations can be used, such as multipleprobe assemblies connected to a single test instrument 140, or multipletransducer arrays 152 used with a single or multiple probe assemblies150 for tandem inspection. Similarly, a test protocol can be performedusing coordination between multiple test instruments 140, such as inresponse to an overall test scheme established from a master testinstrument 140, or established by another remote system such as acomputing facility 108 or general purpose computing device such as alaptop 132, tablet, smart-phone, desktop computer, or the like. The testscheme may be established according to a published standard orregulatory requirement and may be performed upon initial fabrication oron a recurring basis for ongoing surveillance, as illustrative examples.

The receive signal chain of the front-end circuit 122 can include one ormore filters or amplifier circuits, along with an analog-to-digitalconversion facility, such as to digitize echo signals received using theprobe assembly 150. Digitization can be performed coherently, such as toprovide multiple channels of digitized data aligned or referenced toeach other in time or phase. The front-end circuit 122 can be coupled toand controlled by one or more processor circuits, such as a processorcircuit 102 included as a portion of the test instrument 140. Theprocessor circuit 102 can be coupled to a memory circuit, such as toexecute instructions that cause the test instrument 140 to perform oneor more of acoustic transmission, acoustic acquisition, processing, orstorage of data relating to an acoustic inspection, or to otherwiseperform techniques as shown and described herein. The test instrument140 can be communicatively coupled to other portions of the system 100,such as using a wired or wireless communication interface 120.

For example, performance of one or more techniques as shown anddescribed herein can be accomplished on-board the test instrument 140 orusing other processing or storage facilities such as using a computingfacility 108 or a general-purpose computing device such as a laptop 132,tablet, smart-phone, desktop computer, or the like. For example,processing tasks that would be undesirably slow if performed on-boardthe test instrument 140 or beyond the capabilities of the testinstrument 140 can be performed remotely (e.g., on a separate system),such as in response to a request from the test instrument 140.Similarly, storage of data or intermediate data such as A-line matricesof time-series data can be accomplished using remote facilitiescommunicatively coupled to the test instrument 140. The test instrumentcan include a display 110, such as for presentation of configurationinformation or results, and an input device 112 such as including one ormore of a keyboard, trackball, function keys or soft keys,mouse-interface, touch-screen, stylus, or the like, for receivingoperator commands, configuration information, or responses to queries.

The acoustic inspection system 100 can acquire acoustic data, such asusing FMC, half matrix capture (HMC), virtual source aperture (VSA), orplane wave imaging, of a material using an acoustic acquisitiontechnique, such as an acoustic phased array system. The processorcircuit 102 can then generate an acoustic data set, such as a scatteringmatrix (S-matrix), plane wave matrix, or other matrix or data set,corresponding to an acoustic propagation mode, such as pulse echo direct(TT), self-tandem (TT-T), and/or pulse echo with skip (TT-TT).

To generate an image, an acoustic inspection system, such as theacoustic inspection system 100 of FIG. 1, can use inspection parametersand generation parameters. Inspection parameters need to be known, suchas by being input by an operator before a scan begins, without regardsto the final acoustic image to be generated. Inspection parameters caninclude the following: A-scan start (time at the first sample data),sample time resolution, frequency of probe, number of element in probe,and other characteristic of the probe such as element size, pitch, andbandwidth of the probe.

Generation parameters and many inspection parameters are used togenerate an acoustic image from the acoustic data. Generation parameterscan include selected acoustic mode, nominal thickness of part, acousticvelocities of different mode (pressure wave, shear wave, Rayleigh wave)in the different material (part, wedge), and a region of interest (size,position, and/or resolution). An acoustic image, such as a TFM image,can be generated using at least one generation parameter and firstacoustic data, such as FMC data, where the first acoustic data can beacquired at least in part by an acoustic acquisition technique, such asan acoustic phased array system.

In accordance with this disclosure, the system 100 of FIG. 1 canimplement various techniques of this disclosure, including estimating aposition of a probe assembly of a non-destructive inspection system,where the probe assembly is positioned on a material and incommunication with an IMU sensor. The IMU sensor can provide an estimateof a current location of the probe assembly, which can be confirmed bythe probe assembly, using an acoustic signal. In this manner, the dataacquired from the IMU sensor and the probe assembly can be used in acomplementary manner to refine an estimated position of the probeassembly.

The system 100 can use the estimated position of the probe assemblyrelative to the material under inspection along the scan axis in orderto determine the size of the features, e.g., areas of corrosion, lengthof flaw, etc. Using the estimated position, the system 100 canaccurately display, such as on the display 110, an image that representsthe acquired acoustic data depicting the features.

FIG. 2 is a conceptual drawing graphically illustrating a technique totrack a position of a probe assembly of a non-destructive inspectionsystem, such as a phase array ultrasonic testing (PAUT) system, relativeto the surface of the component being inspected, using varioustechniques of this disclosure. In FIG. 2, a processor, such as theprocessor 102 of FIG. 1, can determine the position of a probe assembly,such as the probe assembly 150 of FIG. 1, at a position {right arrowover (x)}_(k) from a 2D image 200 using a previous position {right arrowover (x)}_(k−1) from another 2D image 202 as well as a firstdisplacement estimate {right arrow over (x)}_(k) ^(A) determined usingacoustic data information, such as acquired using the probe assembly 150of FIG. 1, and a second displacement estimate {right arrow over (x)}_(k)^(B) determined using IMU information, such as acquired using the IMUsensor 153 of FIG. 1.

The processor can combine, e.g., such as by averaging, the first andsecond displacement estimates determined using the two types ofmeasurements, e.g., acoustic and IMU. Using the combination, theprocessor can estimate the motion of the probe assembly and generate,using the estimated motion, a second position of the probe assembly at{right arrow over (x)}_(k). Similarly, the processor can determineanother position of the probe assembly at {right arrow over (x)}_(k+1)on a surface S.

In some examples, the techniques shown in FIG. 2 can be accomplishedusing a two-dimensional (2D) matrix array and corrosion mapping, forexample. That is, the probe assembly 150 can include a 2D matrix arrayand the inspection system 100 can generate acoustic images with the 2Dmatrix array at two consecutive times. The inspection system 100 candetermine relevant features (e.g., areas of corrosion, geometrical echo(for welds), grain noise, and volumetric flaws such as cracks, slag,inclusion, and stepwise cracking) common to the acoustic images. Theinspection system 100 can estimate the displacement of the probeassembly 150 using features, e.g., areas of corrosion, common to bothimages. Then, the inspection system 100 can use an IMU measurement, suchas acquired using the IMU sensor 153 in FIG. 1, to improve the estimateof the displacement of the probe assembly 150.

In other examples, the techniques shown in FIG. 2 can be accomplishedusing a linear array and by using synthetic aperture focusing technique(SAFT) principles. An inspection system, such as the inspection system100 of FIG. 1, can perform an acoustic acquisition technique called a“total focusing method” (TFM), such as involving a full-matrix capture(FMC) acquisition scheme where focus can be achieved across a broadspatial region on or within a structure under test. As an example, theprobe assembly 150 can include a linear array and the processor 102 canacquire FMC data using the linear array along a scan axis. The processorcan use an IMU measurement, such as acquired using the IMU sensor 153 inFIG. 1, to estimate the displacement between two consecutiveacquisitions.

In either the two-dimensional (2D) matrix array and feature mappingimplementation or the linear array and SAFT, a position of the probeassembly can be determined using measurements or by using measurementand prediction. These implementations are described in detail below.

FIGS. 3A-3F graphically depict an example of estimating a position of aprobe assembly of an NDT system using a two-dimensional (2D) matrixarray and corrosion mapping. The probe assembly, such as the probeassembly 150 of FIG. 1, can be positioned on a material having anunspecified surface and in communication with an IMU sensor, such as theIMU sensor 153 of FIG. 1.

FIG. 3A is a conceptual drawing graphically illustrating an estimationof a position of a probe movement of a probe assembly using a 2Dacoustic image acquired from a first position of the probe assembly anda 2D acoustic image acquired from a second position of the probeassembly. The probe assembly can be positioned on a material having asurface S and in communication with an IMU sensor.

A first 2D acoustic image 300 can be acquired at position {right arrowover (x)}_(k−1) and a second 2D acoustic image 302 can be acquired atposition {right arrow over (x)}_(k). Using acquired acoustic image dataand IMU sensor measurement data, a processor, such as the processor 102of FIG. 1 can determine the change {right arrow over (x)}_(k−) ^(k)between the two positions.

FIG. 3B depicts an example of a first acoustic data signal, e.g., afirst 2D acoustic image, acquired at a first position of the probeassembly. In particular, FIG. 3B depicts a 2D corrosion image I_(k=0)having an initial state {right arrow over (x)}_(k=0) and where the IMUsensor 153 is zeroed such that {right arrow over (z)}_(k=0) ^(B)=0. Eachsquare in FIG. 3B can represent a pixel. Patches of corrosion in thematerial are shown, where darker pixels indicate thinner material. Inother examples, features other than corrosion can be used. Theprocessor, such as the processor 102 of FIG. 1, can determine a valuethat can represent an amount of the corrosion in each pixel in theimage. Examples of patches of corrosion are shown at 304 and 306.

FIG. 3C depicts an example of a second acoustic data signal, e.g., asecond 2D acoustic image, acquired at a second position of the probeassembly. In particular, FIG. 3C depicts a 2D image I_(k) with corrosionpatches. The patches of corrosion 304, 306, which are common to bothFIG. 3B and FIG. 3C, have moved in FIG. 3C relative to FIG. 3B. In someexamples, the processor can use edge or corner detection techniques totrack the movement of the features, such as the patches of corrosion.The processor can estimate the motion of the probe assembly using theimages from FIGS. 3B and 3C.

FIG. 3D graphically depicts a probability density function (PDF)describing the motion probability of the probe assembly in the x-ydirection. Using Equation 1 below, the processor can perform a 2Dconvolution of the two images from FIGS. 3B and 3C to determine a firstPDF of a first displacement probability from the acoustic data.

P _(k−) ^(k) =f(I _(k−1) *I _(k))  Equation 1:

where {right arrow over (P)}_(k−1) ^(k) is a 2D PDF describing themotion probability of the probe assembly in the x-y direction, I_(k−1)is the image in FIG. 3B, I_(k) is the image in FIG. 3C, and the symbol *represents the mathematical operation of convolution.

In FIG. 3D, the arrow 308 represents an estimated motion of the probeassembly, and the ellipse 310 represents a confidence interval. The PDFcan be a Normal distribution with mean {right arrow over (μ)} andvariance Σ, for example.

As mentioned above, IMU sensor measurements can be used to improve theestimation of the position of the probe assembly. The processor canacquire new IMU sensor measurements {right arrow over (z)}_(k) ^(B).

FIG. 3E graphically depicts a probability density function (PDF) of themotion of the probe assembly in the x-y direction determined using anIMU sensor measurement. In FIG. 3E, the arrow 312 represents theestimated motion of the probe assembly determined using the IMU sensor,and the ellipse 314 represents the confidence interval. In FIG. 3E,{right arrow over (Q)}_(k−1) ^(k) is a 2D PDF describing the motionprobability of the probe assembly in the x-y direction computed usingthe IMU sensor measurement. The PDF can be a Normal distribution withmean {right arrow over (μ)} and variance Σ, for example. In this manner,the processor can determine a second PDF using the IMU sensor, but forthe same probe motion as the first PDF (from the acoustic data).

FIG. 3F is a conceptual drawing graphically illustrating the estimationof the probe assembly from a first position to a second position. Theprocessor can then combine the motion estimate {right arrow over(P)}_(k−1) ^(k) from FIG. 3D and the motion estimate {right arrow over(Q)}_(k−1) ^(k) from FIG. 3E, such as by multiplying the PDFs andnormalizing the results. As seen in FIG. 3F, the combined estimate is asfollows:

{right arrow over (R)} _(k−1) ^(k) ={right arrow over (P)} _(k−1) ^(k)×{right arrow over (Q)} _(k−1) ^(k).

In FIG. 3F, the arrow 316 and the ellipse 318 represent the merged PDFof the IMU sensor and the acoustic data. The arrow 316 represents theestimated motion of the probe assembly and the ellipse 318 representsthe confidence interval.

In some examples, the techniques shown in FIGS. 3A-3F can be repeatedfor each indication (such as 304 and 306 in FIGS. 3B and 3C)individually. The PDF obtained for each indication can then be merged inthe same way as the PDF {right arrow over (P)}_(k−1) ^(k) and {rightarrow over (Q)}_(k−1) ^(k).

The processor can end the scan of the material, such as by a time out orafter using every pixel, for example.

FIG. 4 is a flow diagram 400 depicting an example of estimating aposition of a probe assembly of a non-destructive inspection systemusing a two-dimensional (2D) matrix array and feature mapping, such ascorrosion, without prediction. At block 402, the processor caninitialize the probe assembly, such as having an initial position {rightarrow over (x)}_(k=0) and an initial PDF Σ_(k=0). At the initialposition, the processor can acquire a first acoustic data signal, e.g.,a first acoustic image, of the material using the probe assembly 150 ofFIG. 1.

At block 404, such as after a time step k=k+1, the processor can acquirea second acoustic data signal, e.g., a second acoustic image, of thematerial.

At block 406, the processor can determine a first estimate of adisplacement of the probe assembly between the first and secondpositions using the first and second acoustic data signals. For example,the processor can determine a first PDF that can include the estimatedmotion Δ_(k) ^(A) of the probe assembly and its confidence interval,namely the co-variance matrix Σ_(k) ^(A).

At block 408, such as after the time step k=k+1, the processor canacquire IMU sensor data, such as using the IMU sensor 153 of FIG. 1.

At block 410, the processor can determine a second estimate of thedisplacement of the probe assembly between the first and secondpositions using a signal from the IMU sensor. For example, the processorcan determine a second PDF that can include the estimated motion Δ_(k)^(B) of the probe assembly and its confidence interval, namely theco-variance matrix Σ_(k) ^(B).

At block 412, the processor can combine the first and second estimatesof displacements and estimate, using the combination, a motion of theprobe assembly. For example, the processor can combine the motion andPDF estimates from the acoustic data and IMU sensor data using Equations2 and 3 below:

$\begin{matrix}{{\overset{\rightarrow}{x}}_{k} = {{\overset{\rightarrow}{x}}_{k - 1} + \frac{{\sum_{k}^{B}\Delta_{k}^{A}} + {\sum_{k}^{A}\Delta_{k}^{B}}}{\sum_{k}^{A}{+ \sum_{k}^{B}}}}} & {{Equation}2}\end{matrix}$ $\begin{matrix}{\sum_{k}{= {\sum_{k - 1}{+ \frac{\sum_{k}^{A}\sum_{k}^{B}}{\sum_{k}^{A}{+ \sum_{k}^{B}}}}}}} & {{Equation}3}\end{matrix}$

As seen in the denominators in Equations 2 and 3, if the precision ofthe estimate Σ_(k) ^(A) from an acoustic image is low, more weight isgiven to the IMU sensor data. Using Equations 2 and 3, the processor cangenerate the second state {right arrow over (x)}_(k) of the probeassembly as well as the PDF Σ_(k). In this disclosure, the state of theprobe assembly can include the position, orientation velocity, and/oracceleration.

At decision block 414, the processor can determine whether to end thescan. For example, the processor can determine whether a timer has timedout, whether the region of interest has been inspected, and/or whetherthe positioning measurement is sufficiently precise, e.g., Σ_(k) isgreater than or equal to a threshold of confidence. If the processordetermines that the scan should continue (“NO” branch of block 414), theprocessor can increment the time step k and acquire a new acoustic imageand new IMU data at blocks 404 and 408. If the processor determines thatthe scan should not continue (“YES” branch of block 414), the processorcan stop acquisition at block 416.

It should be noted that although the acquisition of the acoustic imagedata and IMU sensor data is shown in parallel in FIG. 4, in someexamples, the acquisition of acoustic image data and IMU sensor data canbe performed sequentially.

In some example implementations, a predication step can be included,such as described with respect to FIG. 5, to predict a state of theprobe assembly. For example, a processor, such as the processor 102 ofFIG. 1, can use a Bayes filter to perform the prediction. The Bayesfilter can include a Kalman filter, such as a linear Kalman filter, anextended Kalman filter, or an unscented Kalman filter. Althoughdescribed in this disclosure with respect to a linear Kalman filter,other Bayes filters can be used and are considered within the scope ofthis disclosure.

FIG. 5 is a flow diagram 500 depicting an example of estimating aposition of a probe assembly of an NDT system using a two-dimensional(2D) matrix array and corrosion mapping, with prediction. At block 502,the processor can initialize the probe assembly, such as having aninitial (or first) state {right arrow over (x)}(k), such as including aposition x(k) and a velocity {dot over (x)}(k), as shown in Equation 4below:

$\begin{matrix}{{\overset{\rightarrow}{x}(k)} = \begin{bmatrix}{x(k)} \\{\overset{˙}{x}(k)}\end{bmatrix}} & {{Equation}4}\end{matrix}$

In addition, the initial state of the probe assembly can include acovariance matrix, such as shown in Equation 5 below:

$\begin{matrix}{{P(k)} = \begin{bmatrix}\sum_{xx} & \sum_{x\overset{˙}{x}} \\\sum_{\overset{˙}{x}x} & \sum_{\overset{˙}{x}\overset{˙}{x}}\end{bmatrix}} & {{Equation}5}\end{matrix}$

where Σ represents a co-variance matrix of a PDF. At the initialposition, the processor can acquire a first acoustic data signal, e.g.,a first acoustic image, of the material using the probe assembly 150 ofFIG. 1.

At block 504, such as after a time step k=k+1, the processor, such asthe processor 102 of FIG. 1, can predict a second state of the probeassembly. For example, the processor can predict a second state, such asincluding a position and/or orientation, using previously determinedmotion components, such as using a physical model of system motion. Forexample, the processor can use a state model A (a physical model ofsystem motion) to predict the state at time k+1 using information fromthe previous time k. The state model A represents a set of equationsthat allows the computation of the state at k+1, from the variable at k.The processor can predict the second state using previously determinedmotion components, such as predetermined speed, predetermined direction,and a sampling rate, e.g., 60 Hertz, using Equations 6 and 7 below.

The state x of the probe assembly at the second position is given byEquation 6:

{right arrow over ({circumflex over (x)})}(k|k−1)=A{right arrow over(x)}(k−1)

where A is the state model, such as input by the user, {right arrow over(x)}(k) is the estimate of the variable x, (k|k−1) represents attimestep k, knowing its value at timestep k−1, and {right arrow over({circumflex over (x)})}(k|k−1) corresponds to the estimate of state xat timestep k, knowing state x at timestep k−1. The covariance P isgiven by Equation 7:

{right arrow over (P)}(k|k−1)=AP(k−1)A ^(T) +Q

where A is the state model, such as input by the user, A^(T) is thetranspose matrix of A, and Q is the state model noise, such as input bythe user.

At block 506, the processor can acquire a second acoustic data signal,e.g., a second acoustic image, of the material. The processor can use aninverse of the acoustic sensor model (H_(A)) such as input by the user,to update the predicted state {right arrow over ({circumflex over(x)})}(k|k−1) with the second acoustic measurement {right arrow over(z)}_(A)(k) using Equations 8-12 below:

Equation 8 is given by:

{right arrow over (y)} _(A)(k)={right arrow over (z)} _(A)(k)−(H_(A){right arrow over ({circumflex over (x)})}(k|k−1))  Innovation:

where (H_(A){right arrow over ({circumflex over (x)})}(k|k−1))represents the measurement if the predicted state was correct. Theinnovation (or residual) represents a difference between the predictedstate and state determined by the acoustic measurement {right arrow over(z)}_(A)(k).

Equation 9 is given by:

S(k|k−1,z _(A)(k))=(H _(A) {right arrow over (P)}(k|k−1)H _(A) ^(T))+R_(A)  Variance Update:

where the variance S is updated using the previously obtained covarianceP modified by the inverse of the acoustic sensor model (H_(A)), thetranspose matrix of H_(A) (H_(A) ^(T)), and the acoustic sensor noisemodel R_(A), such as input by the user.

Equation 10 is given by:

K _(A)(k)={right arrow over (P)}(k|k−1)H _(A) S(k|k−1,{right arrow over(z)} _(A)(k))  Kalman Gain Matrix:

where the Kalman gain matrix K_(A)(k) is the product of the covariancematrix P, the inverse of the acoustic sensor model (H_(A)), and thevariance S.

Equation 11 is given by:

{right arrow over ({circumflex over (x)})}(k|k−1,{right arrow over (z)}_(A)(k))={right arrow over ({circumflex over (x)})}(k|k−1)+K_(A)(k){right arrow over (y)} _(A)(k)  Update State Prediction:

The predicted state {right arrow over ({circumflex over (x)})}(k|k−1)from Equation 6 is updated by adding the Kalman gain matrix K_(A)(k)multiplied by the innovation y.

Equation 12 is given by:

{right arrow over (y)} _(B)(k|k−1,{right arrow over (z)} _(A)(k))=(I−K_(A)(k)H _(A)){right arrow over (P)}(k|k−1)  Update Covariance Matrix:

The predicted covariance P from Equation 7 is updated using the identitymatrix I, the Kalman gain matrix K_(A)(k), and the inverse of theacoustic sensor model (H_(A)).

Next, the IMU sensor data can be acquired. At block 508, the processorcan acquire IMU sensor data and determine a second estimate of thedisplacement of the probe between the first and second positions using asignal from the IMU sensor and a physical model. Using Equations 13-17,which are similar to Equations 8-12, the processor can update thepredicted state determined by Equation 11.

Equation 13 is given by:

{right arrow over (y)} _(B)(k)={right arrow over (z)} _(B)(k)−(H_(B){right arrow over ({circumflex over (x)})}(k|k−1,{right arrow over(z)} _(A)(k)))  Innovation:

where an IMU sensor model H_(B), such as input by the user, can updatethe predicted state determined by Equation 11. The innovation y is thedifference between the IMU sensor measurement {right arrow over(z)}_(B)(k) and the updated predicted state term.

Equation 14 is given by:

S(k|k−1,{right arrow over (z)} _(A)(k),{right arrow over (z)}_(B)(k))=(H _(B) {right arrow over (P)}(k|k−1,{right arrow over (z)}_(A)(k))H _(B) ^(T))+R _(B)  Variance Update:

where the variance S is updated using the previously obtained covarianceP modified by the inverse of the IMU sensor model (H_(B)), the transposematrix of H_(B) (H_(B) ^(T)), and the IMU sensor noise model R_(B), suchas input by the user.

Equation 15 is given by:

K _(B)(k)={right arrow over (P)}(k|k−1,{right arrow over (z)} _(A)(k))H_(B) S(k|k−1,{right arrow over (z)} _(A)(k),{right arrow over (z)}_(B)(k))  Kalman Gain Matrix:

where the Kalman gain matrix K_(B)(k) is the product of the covariancematrix P, the inverse of the IMU sensor model (H_(B)), and the updatedvariance S.

Equation 16 is given by:

{right arrow over ({circumflex over (x)})}(k|k−1,{right arrow over (z)}_(A)(k),{right arrow over (z)} _(B)(k))={right arrow over ({circumflexover (x)})}(k|k−1,{right arrow over (z)} _(A)(k))+K _(B)(k){right arrowover (y)} _(B)(k)  Update State Prediction:

The predicted state {right arrow over ({circumflex over (x)})}(k|k−1,{right arrow over (z)}_(A)(k)) from Equation 11 is updated by adding theKalman gain matrix K_(B)(k) multiplied by the innovation y.

Equation 17 is given by:

{right arrow over (P)}(k|k−1,{right arrow over (z)} _(A)(k),{right arrowover (z)} _(B)(k))=(I−K _(B)(k)H _(B)){right arrow over(P)}(k|k−1,{right arrow over (z)} _(A)(k))  Update Covariance Matrix:

The predicted covariance P from Equation 12 is updated using theidentity matrix I, the Kalman gain matrix K_(B)(k), and the inverse ofthe IMU sensor model (H_(B)).

Using the equations above, including Equations 16 and 17, the processorcan predict the second position using the previously determined motioncomponents {right arrow over (z)}_(A)(k) and {right arrow over(z)}_(B)(k) and can combine the first and second estimates ofdisplacement and can estimate, using the combination, a motion of theprobe assembly.

At block 510, the processor can generate, using the estimated motion,the second state of the probe assembly and output the second state. Forexample, the processor can output the second state using the stateprediction of Equation 16 and the covariance matrix of Equation 17.

At decision block 512, the processor can determine whether to end thescan. For example, the processor can determine whether a timer has timedout, whether the region of interest has been inspected, and/or whetherthe positioning measurement is sufficiently precise, e.g., Σ_(k) isgreater than or equal to a threshold of confidence. If the processordetermines that the scan should continue (“NO” branch of block 512), theprocessor can increment the time step k and perform a new prediction atblock 504 and continue with the flow diagram 500 as describe above. Ifthe processor determines that the scan should not continue (“YES” branchof block 512), the processor can stop acquisition at block 514.

It should be noted that although the acquisition of the acoustic imagedata was performed prior to acquisition IMU sensor data in FIG. 5, insome examples, the acquisition of acoustic image data can be performedafter acquisition of the IMU sensor data.

As mentioned above, the techniques shown in FIG. 2 can be accomplishedby using a two-dimensional (2D) matrix array and corrosion mapping, suchas described in FIGS. 3A-3F, or by using a linear array probe assemblyin communication with an IMU sensor and by using SAFT principles, suchas shown in FIG. 6.

FIG. 6 is a conceptual diagram illustration an example of using SAFTprinciples to track a position of a probe assembly of a non-destructiveinspection system, such as a phase array ultrasonic testing (PAUT)system, relative to the surface of the component being inspected usingvarious techniques of this disclosure. A material 600 having a surface602 is shown in FIG. 6. A probe assembly 604, such as a linear arrayprobe assembly, is shown at a first position 606. The probe assembly 604can be an example of the probe assembly 150 of FIG. 1. The probeassembly 604 can be in communication with an IMU sensor, such as the IMUsensor 153 in FIG. 1.

Features 608A-608C, such as flaws, geometrical echoes (for welds), grainnoises, and volumetric flaws such as cracks, slag, inclusion, orstepwise cracking, are shown in the material 600. The probe assembly 604can be moved along the surface 602 of the material 600 to positions 606,610, 612, and 614. Using various techniques of this disclosure, aprocessor can determine an estimate of a position of the probe assembly604 using TOF information and then refine that estimated position usinginformation from the IMU sensor using SAFT techniques.

In SAFT, the transmitted beam is a broad band signal which is sent outin a wide cone of transmission, which can be achieved by a smallelevation of the probe elements, such as around half of the wavelengthin the wedge of the probe. The broadband nature of the transmittedsignal allows direct measurement of the time-of-flight (TOF) or thephase information of the signal, thereby allowing the determination ofthe range of any reflectors (e.g., changes in acoustical impedance)which cause returning echoes. The arrows 616-620 represent the TOFs atposition 614 to the features 608A-608C, respectively.

For each scan position, the processor can determine 3D acoustic imagedata, such as TFM image data. The 3D acoustic image data can bedetermined using acoustic data, such as FMC data, in the probe axis andSAFT information in the scan axis. The processor can then determine theacoustic peaks in the determined 3D acoustic image data that correspondto the features 608A-608C, where the features can be any feature thatreflects the acoustic signal. Using the determined acoustic peaks, theprocessor can then acquire the FMC data and IMU data for the new scanposition. That is, at a new scan position, the processor can add the newposition to the beamforming and determine how much the new positioncontributes to the amplitude of the acoustic peaks. The processor canthen determine the position increment that provides the best overallincrease of the peak amplitude, which can be an iterative process basedon the IMU estimates. Once the processor has refined the positionoriginally estimated using TOF with the IMU sensor information, the“new” position can become a “previously known position” and cancontribute to the new image. The probe assembly can be moved to the nextscan position and the process can be repeated.

As graphically depicted in FIG. 6, a user, for example, can move theprobe assembly 604 over the first features 608A-608C, and the inspectionsystem, such as the inspection system 100 of FIG. 1, can detect thefirst features 608A-608C in the acoustic data signal. The TOFs to thefirst features 608A-608C can vary depending on where the probe assembly604 is relative to the first features 608A-608C. In FIG. 6, positions606, 610, and 612 can be “previously known positions” in that theirpositions have already been refined using IMU sensor data. The processorcan acquire, at the first position 612 of the probe assembly, a firstacoustic data signal of the material 600. The processor can determine,at the first position 612, a first TOF to a first feature in thematerial 600 using the first acoustic data signal. In some examples,such as in FIG. 6, the processor can determine more than one TOF at thefirst position 612 using the first acoustic data signal, such as in FIG.6 where the three TOFs each correspond to the three first features608A-608C shown in FIG. 6.

The user can then move the probe assembly 604 to the second position 614by an unknown position increment 616. The processor can acquire, at thesecond position 614 of the probe assembly, a second acoustic data signalof the material 600. The processor can determine, at the second position614, a second TOF to the second feature in the material 600 using thesecond acoustic data signal. In some examples, the processor candetermine more than one TOF at the second position 614 using the secondacoustic data signal, such as in FIG. 6 where the three TOFs eachcorrespond to the three second features in the material, where the firstand second features are the same features, such as the three features608A-608C shown in FIG. 6. The second TOFs are represented by arrows616-620.

The processor can determine 3D acoustic image data, such as TFM imagedata in the scan axis to determine a match between the first and secondTOFs at the corresponding first and second positions 612, 614. Theprocessor can use the data acquired at the previously known positions606 and 610 to determine the 3D acoustic image data. The 3D acousticimage data can be determined using acoustic data, such as FMC data, inthe probe axis and SAFT information in the scan axis, such as using aTFM beamforming process. The processor can then determine the acousticpeaks in the 3D acoustic image data that correspond to the features608A-608C.

In examples in which the processor determined two or more TOFs at thefirst position 606 and two or more TOFs at the second position 610, theprocessor can determine a first estimate of the displacement of theprobe assembly based on a difference between the plurality of first TOFsat the first position and the plurality of second TOFs at the secondposition, such as using an average of the plurality of the first andsecond TOFs. For example, each TOF can have its own signature so theprocessor can compare corresponding TOFs.

To refine the first estimate of the displacement of the probe assemblydetermined using TOF, the processor can use IMU sensor data acquiredusing the IMU sensor. For example, the processor can determine a secondestimate of the displacement of the probe assembly 604 between the firstand second positions 612, 614 using a signal from the IMU sensor. As anexample, the processor can include the data from the new position 614into the beamformed image. Then, the processor can determine the secondestimate of the displacement of the probe assembly, e.g., the positionincrement 616 in FIG. 6, by determining the position that maximizes anincrease in the amplitude of the acoustic peaks in the determined 3Dacoustic image data that correspond to the features 608A-608C. Theprocessor can then combine the first and second estimates ofdisplacement, such as by averaging or by using another central tendency,and estimate, using the combination, a motion of the probe assembly. Theprocessor can then generate, using the estimated motion, the secondposition of the probe assembly.

By using the techniques of FIG. 6, the IMU sensor and SAFT principlescan complement one another to provide an estimate of a current locationof the probe assembly.

FIG. 7 is a flow diagram depicting an example of estimating a positionof a probe assembly of an NDT system using an ultrasonic probe arraypositioned on a material and in communication with an IMU sensor, inaccordance with this disclosure. The flow diagram 700 shown in FIG. 7 isapplicable to techniques that use a two-dimensional (2D) matrix arrayand corrosion mapping, for example, as well as techniques that use alinear array and SAFT principles, each technique being described abovein detail.

At block 702, a processor of an inspection system, such as the processor102 of the inspection system 100 of FIG. 1, can acquire, at a firstposition of the probe assembly, a first acoustic data signal of thematerial using the probe assembly. At block 704, the processor canacquire, at a second position of the probe assembly, a second acousticdata signal of the material using the probe assembly;

At block 706, the processor can determine a first estimate of adisplacement of the probe assembly between the first and secondpositions using the first and second acoustic data signals, which, insome examples, can include determining a first probability densityfunction of a first displacement probability.

At block 708, the processor can determine a second estimate of thedisplacement of the probe assembly between the first and secondpositions using a signal from the IMU sensor and, in some examples,using a physical model of system motion, such as including a previouslydetermined speed, a previously determined direction, and a samplingrate. In some examples, the processor can determine the second estimateby determining a second probability density function of a seconddisplacement probability.

At block 710, the processor can combine the first and second estimatesof displacements.

At block 712, the processor can estimate, using the combination, amotion of the probe assembly.

At block 714, the processor can generate, using the estimated motion,the second position of the probe assembly.

In some examples, such as when using 2D matrix array probe assembly, theprocessor can generate a first acoustic image using the first acousticdata signal and generate a second acoustic image using the secondacoustic data signal. The processor can then determine the firstestimate of the displacement of the probe assembly between the first andsecond positions using a feature common to both the first and secondacoustic images. In some examples, the material under test can include ametal pipe and the feature can include corrosion.

In some examples, such as when using a linear array with SAFT, theprocessor can determine, at the first position, a first time-of-flight(TOF) to a feature in the material using the first acoustic data signal,and can determine, at the second position, a second TOF to the featurein the material using the second acoustic data signal. The processor canthen determine the first estimate of the displacement of the probeassembly between the first and second positions using the first TOF andthe second TOF.

In some examples, such as when using a linear array with SAFT, theprocessor can determine, at the first position, a plurality of firsttime-of-flights corresponding to individual ones of a plurality of firstfeatures in the material using the first acoustic data signal, and candetermine, at the second position, a plurality of second time-of-flightscorresponding to individual ones of a plurality of second features inthe material using the second acoustic data signal.

The processor can determining the first estimate of the displacement ofthe probe assembly between the first and second positions using thefirst and second acoustic data signals by determining the first estimateof the displacement of the probe assembly based on the plurality offirst time-of-flights and determining the second estimate of thedisplacement of the probe assembly based on the plurality of secondtime-of-flights.

In some examples, a prediction step can be included. For example, theprocessor can predict the second position using previously determinedmotion components and combine the first and second estimates ofdisplacements by combining the first and second estimates ofdisplacement and the predicted second position. For example, theprocessor can predict the second position using a physical model ofsystem motion, such as using a previously determined speed, a previouslydetermined direction, and a sampling rate.

FIG. 8 is an example of a linear array that can be used to implementvarious techniques of this disclosure. The linear array 800 shown canform part of the transducer array 152 of FIG. 1.

FIG. 9 is an example of a two-dimensional (2D) matrix array that can beused to implement various techniques of this disclosure. Thetwo-dimensional (2D) matrix array 900 shown can form part of thetransducer array 152 of FIG. 1.

VARIOUS NOTES

Each of the non-limiting aspects or examples described herein may standon its own, or may be combined in various permutations or combinationswith one or more of the other examples.

The above detailed description includes references to the accompanyingdrawings, which form a part of the detailed description. The drawingsshow, by way of illustration, specific embodiments in which theinvention may be practiced. These embodiments are also referred toherein as “examples.” Such examples may include elements in addition tothose shown or described. However, the present inventors alsocontemplate examples in which only those elements shown or described areprovided. Moreover, the present inventors also contemplate examplesusing any combination or permutation of those elements shown ordescribed (or one or more aspects thereof), either with respect to aparticular example (or one or more aspects thereof), or with respect toother examples (or one or more aspects thereof) shown or describedherein.

In the event of inconsistent usages between this document and anydocuments so incorporated by reference, the usage in this documentcontrols.

In this document, the terms “a” or “an” are used, as is common in patentdocuments, to include one or more than one, independent of any otherinstances or usages of “at least one” or “one or more.” In thisdocument, the term “or” is used to refer to a nonexclusive or, such that“A or B” includes “A but not B,” “B but not A,” and “A and B,” unlessotherwise indicated. In this document, the terms “including” and “inwhich” are used as the plain-English equivalents of the respective terms“comprising” and “wherein.” Also, in the following aspects, the terms“including” and “comprising” are open-ended, that is, a system, device,article, composition, formulation, or process that includes elements inaddition to those listed after such a term in an aspect are still deemedto fall within the scope of that aspect. Moreover, in the followingaspects, the terms “first,” “second,” and “third,” etc. are used merelyas labels, and are not intended to impose numerical requirements ontheir objects.

Method examples described herein may be machine or computer-implementedat least in part. Some examples may include a computer-readable mediumor machine-readable medium encoded with instructions operable toconfigure an electronic device to perform methods as described in theabove examples. An implementation of such methods may include code, suchas microcode, assembly language code, a higher-level language code, orthe like. Such code may include computer readable instructions forperforming various methods. The code may form portions of computerprogram products. Further, in an example, the code may be tangiblystored on one or more volatile, non-transitory, or non-volatile tangiblecomputer-readable media, such as during execution or at other times.Examples of these tangible computer-readable media may include, but arenot limited to, hard disks, removable magnetic disks, removable opticaldisks (e.g., compact discs and digital video discs), magnetic cassettes,memory cards or sticks, random access memories (RAMs), read onlymemories (ROMs), and the like.

The above description is intended to be illustrative, and notrestrictive. For example, the above-described examples (or one or moreaspects thereof) may be used in combination with each other. Otherembodiments may be used, such as by one of ordinary skill in the artupon reviewing the above description. The Abstract is provided to complywith 37 C.F.R. § 1.72(b), to allow the reader to quickly ascertain thenature of the technical disclosure. It is submitted with theunderstanding that it will not be used to interpret or limit the scopeor meaning of the aspects. Also, in the above Detailed Description,various features may be grouped together to streamline the disclosure.This should not be interpreted as intending that an unclaimed disclosedfeature is essential to any aspect. Rather, inventive subject matter maylie in less than all features of a particular disclosed embodiment.Thus, the following aspects are hereby incorporated into the DetailedDescription as examples or embodiments, with each aspect standing on itsown as a separate embodiment, and it is contemplated that suchembodiments may be combined with each other in various combinations orpermutations. The scope of the invention should be determined withreference to the appended aspects, along with the full scope ofequivalents to which such aspects are entitled.

The claimed invention is:
 1. A method of estimating a position of aprobe assembly of a non-destructive inspection system, the probeassembly positioned on a material and in communication with an inertialmeasurement unit (IMU) sensor, the method comprising: acquiring, at afirst position of the probe assembly, a first acoustic data signal ofthe material using the probe assembly; acquiring, at a second positionof the probe assembly, a second acoustic data signal of the materialusing the probe assembly; determining a first estimate of a displacementof the probe assembly between the first and second positions using thefirst and second acoustic data signals; determining a second estimate ofthe displacement of the probe assembly between the first and secondpositions using a signal from the IMU sensor; combining the first andsecond estimates of displacements; estimating, using the combination, amotion of the probe assembly; and generating, using the estimatedmotion, the second position of the probe assembly.
 2. The method ofclaim 1, wherein determining the first estimate of the displacement ofthe probe assembly includes determining a first probability densityfunction of a first displacement probability, and wherein determiningthe second estimate of the displacement of the probe assembly includesdetermining a second probability density function of a seconddisplacement probability.
 3. The method of claim 1, further comprising:generating a first acoustic image using the first acoustic data signal;and generating a second acoustic image using the second acoustic datasignal, wherein determining the first estimate of the displacement ofthe probe assembly between the first and second positions using thefirst and second acoustic data signals includes: determining the firstestimate of the displacement of the probe assembly between the first andsecond positions using at least one feature common to both the first andsecond acoustic images.
 4. The method of claim 3, wherein the materialis a pipe, and wherein the feature includes corrosion.
 5. The method ofclaim 1, comprising: determining, at the first position, a firsttime-of-flight (TOF) to a feature in the material using the firstacoustic data signal; and determining, at the second position, a secondTOF to the feature in the material using the second acoustic datasignal, and wherein determining the first estimate of the displacementof the probe assembly between the first and second positions using thefirst and second acoustic data signals includes: determining the firstestimate of the displacement of the probe assembly between the first andsecond positions using the first TOF and the second TOF.
 6. The methodof claim 1, further comprising: determining, at the first position andusing the first acoustic data signal, a plurality of firsttime-of-flights that each correspond to a plurality of first features inthe material; and determining, at the second position and using thesecond acoustic data signal, a plurality of second time-of-flights thateach correspond to a plurality of second features in the material,wherein the second features are the same as the first features, andwherein determining the first estimate of the displacement of the probeassembly between the first and second positions using the first andsecond acoustic data signals includes: determining the first estimate ofthe displacement of the probe assembly using a difference between theplurality of first time-of-flights and the second time-of-flights. 7.The method of claim 1, further comprising: predicting the secondposition, wherein combining the first and second estimates ofdisplacements includes combining the first and second estimates ofdisplacement and the predicted second position.
 8. The method of claim7, wherein predicting the second position includes: predicting thesecond position using a previous system state and a physical model ofsystem motion.
 9. The method of claim 8, wherein predicting the secondposition using the physical model of system motion includes: predictingthe second position using a previously determined speed, a previouslydetermined direction, and a sampling rate.
 10. An ultrasound inspectionsystem for estimating a position of an ultrasonic probe assembly of anon-destructive inspection system, the system comprising: the ultrasonicprobe assembly to be positioned on a material and in communication withan inertial measurement unit (IMU) sensor; and a processor configuredto: acquire, at a first position of the probe assembly, a first acousticdata signal of the material using the probe assembly; acquire, at asecond position of the probe assembly, a second acoustic data signal ofthe material using the probe assembly; determine a first estimate of adisplacement of the probe assembly between the first and secondpositions using the first and second acoustic data signals; determine asecond estimate of the displacement of the probe assembly between thefirst and second positions using a signal from the IMU sensor; combinethe first and second estimates of displacements; estimate, using thecombination, a motion of the probe assembly; and generate, using theestimated motion, the second position of the probe assembly.
 11. Thesystem of claim 10, wherein the processor configured to determine thefirst estimate of the displacement of the probe assembly is configuredto determine a first probability density function of a firstdisplacement probability, and wherein the processor configured todetermine the second estimate of the displacement of the probe assemblyis configured to determine a second probability density function of asecond displacement probability.
 12. The system of claim 10, wherein theprocessor is configured to: generate a first acoustic image using thefirst acoustic data signal; and generate a second acoustic image usingthe second acoustic data signal, wherein the processor configured todetermine the first estimate of the displacement of the probe assemblybetween the first and second positions using the first and secondacoustic data signals is configured to: determine the first estimate ofthe displacement of the probe assembly between the first and secondpositions using at least one feature common to both the first and secondacoustic images.
 13. The system of claim 12, wherein the material is apipe, and wherein the feature includes corrosion.
 14. The system ofclaim 10, the processor configured to: determine, at the first position,a first time-of-flight (TOF) to a feature in the material using thefirst acoustic data signal; and determine, at the second position, asecond TOF to the feature in the material using the second acoustic datasignal, wherein the processor configured to determine the first estimateof the displacement of the probe assembly between the first and secondpositions using the first and second acoustic data signals is configuredto: determine the first estimate of the displacement of the probeassembly between the first and second positions using the first TOF andthe second TOF.
 15. The system of claim 10, the processor configured to:determine, at the first position and using the first acoustic datasignal, a plurality of first time-of-flights that each correspond to aplurality of first features in the material; and determine, at thesecond position and using the second acoustic data signal, a pluralityof second time-of-flights that each correspond to a plurality of secondfeatures in the material, wherein the second features are the same asthe first features, wherein the processor configured to determine thefirst estimate of the displacement of the probe assembly between thefirst and second positions using the first and second acoustic datasignals is configured to: determine the first estimate of thedisplacement of the probe assembly using a difference between theplurality of first time-of-flights and the second time-of-flights. 16.The system of claim 10, the processor configured to: predict the secondposition, wherein the processor configured to combine the first andsecond estimates of displacements is configured to combine the first andsecond estimates of displacement and the predicted second position. 17.The system of claim 16, wherein the processor configured to predict thesecond position is configured to: predict the second position using aprevious system state and a physical model of system motion.
 18. Thesystem of claim 17, wherein the processor configured to predict thesecond position using the physical model of system motion is configuredt: predict the second position using a previously determined speed, apreviously determined direction, and a sampling rate.